|Sabertooth has it right in one.|
To expand a little on that, the router will mask the true IP address with one that which it gets from the ISP.
For example: if true IP is 22.214.171.124
Router will show something like: 126.96.36.199
Even better is to compliment the router with a good software firewall that will monitor programs trying to access the net from within.
Sorta like a jail :-)
Router keeps the bad eggs out. Software firewall prevents those that are in from getting out.